Inverse-free solution to inverse kinematics of two-wheeled mobile robot system using gradient dynamics method

To avoid Jacobian inversion existing in the conventional pseudo inverse solution effectively and to obtain the solution of minimum two-norm tracking error to the inverse kinematics of the two-wheeled mobile robot system (TWMRS), an inverse-free solution using gradient dynamics (GD) method is presented and investigated in this paper. As we probably know, the inversion of Jacobian matrix is required in the pseudo inverse method when solving the problem, which is computationally intensive, especially for complex mobile robot systems. Besides, to take full advantage of the mutual coordination effect between a mobile platform with two omni-directional driving wheels and a six-joint manipulator, an integrated kinematics of the TWMRS is derived and developed to coordinate the motions of the platform and the manipulator. In addition, such an inverse-free solution with different values of design parameter and the conventional pseudo inverse solution are performed for comparison based on the TWMRS for specific path-tracking tasks. The illustrative and comparative simulation results show that the mobile platform and the manipulator coordinate well during the whole process with the aid of the integrated kinematics, and then substantiate the efficacy, accuracy as well as superiority of the proposed inverse-free solution to inverse kinematics of the TWMRS.